cf. [1]}. For the Bessel functions occurring in the Riccati-Bessel-functions \(\xi _n(z)\)  and \(\psi _n(z)\)  follows from this with the weight \(\alpha = n + \frac{1}{2}\)  that
\(\dot{\xi _n}(z) & = \sqrt{\textstyle {\frac{\pi }{2}}}\sqrt{z}\left(J_{n - \frac{1}{2}}(z) - \frac{n}{z}J_{n + \frac{1}{2}}(z)\right) \\\text{and} \quad \dot{\psi _n}(z) & = \sqrt{\textstyle {\frac{\pi }{2}}}\sqrt{z}\left(J_{n - \frac{1}{2}}(z) - \frac{n}{z}J_{n + \frac{1}{2}}(z)\right) + \sqrt{\textstyle {\frac{\pi }{2}}}\sqrt{z}\left(Y_{n - \frac{1}{2}}(z) - \frac{n}{z}Y_{n + \frac{1}{2}}(z)\right)i \) 
